Count the balls off the brass monkey def pyramid blocks (n, m, h): Mysteries of the pyramids have fascinated humanity through the ages. Instead of packing your machete and pith helmet to trek through deserts and jungles to raid the hidden treasures of the ancients like some Indiana Croft, or by gaining visions of enlightenment by intensely meditating under the apex set over a square base like some Deepak Veidt, this problem deals with something a bit more mundane; truncated brass monkeys of layers of discrete uniform spheres, in spirit of that spherical cow running in a vacuum. Given that the top layer of the truncated brass monkey consists of n rows and m columns of spheres, and each solid layer immediately below the one above it always contains one more row and one more column, how many spheres in total make up this truncated brass monkey that has h layers? This problem could be solved in a straightforward brute force fashion by mechanistically tallying up the spheres iterated through these layers. However, the just reward for naughty boys and girls who take such a blunt approach is to get to watch the automated tester take roughly a minute to terminate! Some creative use of discrete math and summation formulas gives an analytical closed form formula that makes the answers come out faster than you can snap your fingers simply by plugging the values of n, m and h into this formula. n m h Expected result 2 3 1 6 2 3 10 570 10 11 12 3212 100 100 100 2318350 10**6 10**6 10**6 2333331833333500000 As an unrelated random note, Wolfram is a great language with great online documentation. You can play with this language for free on Wolfram Cloud to evaluate not just examples from the tutorials, but fully symbolic Wolfram expressions such as Sum[ (n+i) (m+i), (i, 0, h-1}].
Count the balls off the brass monkey def pyramid blocks (n, m, h): Mysteries of the pyramids have fascinated humanity through the ages. Instead of packing your machete and pith helmet to trek through deserts and jungles to raid the hidden treasures of the ancients like some Indiana Croft, or by gaining visions of enlightenment by intensely meditating under the apex set over a square base like some Deepak Veidt, this problem deals with something a bit more mundane; truncated brass monkeys of layers of discrete uniform spheres, in spirit of that spherical cow running in a vacuum. Given that the top layer of the truncated brass monkey consists of n rows and m columns of spheres, and each solid layer immediately below the one above it always contains one more row and one more column, how many spheres in total make up this truncated brass monkey that has h layers? This problem could be solved in a straightforward brute force fashion by mechanistically tallying up the spheres iterated through these layers. However, the just reward for naughty boys and girls who take such a blunt approach is to get to watch the automated tester take roughly a minute to terminate! Some creative use of discrete math and summation formulas gives an analytical closed form formula that makes the answers come out faster than you can snap your fingers simply by plugging the values of n, m and h into this formula. n m h Expected result 2 3 1 6 2 3 10 570 10 11 12 3212 100 100 100 2318350 10**6 10**6 10**6 2333331833333500000 As an unrelated random note, Wolfram is a great language with great online documentation. You can play with this language for free on Wolfram Cloud to evaluate not just examples from the tutorials, but fully symbolic Wolfram expressions such as Sum[ (n+i) (m+i), (i, 0, h-1}].
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Question
![Count the balls off the brass monkey
def pyramid_blocks (n, m, h):
Mysteries of the pyramids have fascinated humanity through the ages. Instead of packing your
machete and pith helmet to trek through deserts and jungles to raid the hidden treasures of the
ancients like some Indiana Croft, or by gaining visions of enlightenment by intensely meditating
under the apex set over a square base like some Deepak Veidt, this problem deals with something a
bit more mundane; truncated brass monkeys of layers of discrete uniform spheres, in spirit of that
spherical cow running in a vacuum.
Given that the top layer of the truncated brass monkey consists of n rows and m columns of spheres,
and each solid layer immediately below the one above it always contains one more row and one
more column, how many spheres in total make up this truncated brass monkey that has h layers?
This problem could be solved in a straightforward brute force fashion by mechanistically tallying
up the spheres iterated through these layers. However, the just reward for :
who take such a blunt approach is to get to watch the automated tester take roughly a minute to
terminate! Some creative use of discrete math and summation formulas gives an analytical closed
form formula that makes the answers come out faster than you can snap your fingers simply by
plugging the values of n, m and h into this formula.
ughty boys and girls
Expected result
m
h
2
1
6
2
3
10
570
10
11
12
3212
100
100
100
2318350
10**6
10**6
10**6
2333331833333500000
As an unrelated random note, Wolfram is a great language with great online documentation. You can
play with this language for free on Wolfram Cloud to evaluate not just examples from the tutorials,
but fully symbolic Wolfram expressions such as Sum[ (n+i) (m+i), (i, 0, h-1}].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F886e41a3-9447-40ef-9864-5f77f8e5f654%2F45cb4178-28d4-415b-8163-45b04db6fa42%2Fyow23zm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Count the balls off the brass monkey
def pyramid_blocks (n, m, h):
Mysteries of the pyramids have fascinated humanity through the ages. Instead of packing your
machete and pith helmet to trek through deserts and jungles to raid the hidden treasures of the
ancients like some Indiana Croft, or by gaining visions of enlightenment by intensely meditating
under the apex set over a square base like some Deepak Veidt, this problem deals with something a
bit more mundane; truncated brass monkeys of layers of discrete uniform spheres, in spirit of that
spherical cow running in a vacuum.
Given that the top layer of the truncated brass monkey consists of n rows and m columns of spheres,
and each solid layer immediately below the one above it always contains one more row and one
more column, how many spheres in total make up this truncated brass monkey that has h layers?
This problem could be solved in a straightforward brute force fashion by mechanistically tallying
up the spheres iterated through these layers. However, the just reward for :
who take such a blunt approach is to get to watch the automated tester take roughly a minute to
terminate! Some creative use of discrete math and summation formulas gives an analytical closed
form formula that makes the answers come out faster than you can snap your fingers simply by
plugging the values of n, m and h into this formula.
ughty boys and girls
Expected result
m
h
2
1
6
2
3
10
570
10
11
12
3212
100
100
100
2318350
10**6
10**6
10**6
2333331833333500000
As an unrelated random note, Wolfram is a great language with great online documentation. You can
play with this language for free on Wolfram Cloud to evaluate not just examples from the tutorials,
but fully symbolic Wolfram expressions such as Sum[ (n+i) (m+i), (i, 0, h-1}].
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